Project 1

Abstract

This project is all about analysing the SWDEFECTS file using R and probability theory. You will need to change the headings to reflect the nature of the project intentions. Re write this abstract as the last thing you do.

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1 Introduction to the data

1.1 Data and variables(see MS pg. 77,125)

Describe the data and the problem we wish to investigate. In this case it is NASA or we can say any company that they are collecting data we would like to know if the data that they are collecting is right and following by that we would like to know if the software or code that we are using to collect data is working precise without any fault.

So, the question is how can we do that? There are many ways to see if the collected data is right or wrong which in this case we are considering 4 different methods to see if their prediction of faulty data is right or wrong. These methods should be applied to collected data.

The data is constructed from the data fromt the satelite and if there is any defect and the prediction of each alorithm and what they say. If there is any defect in the data then it is TRUE and if there is not it is FALSE

In this project we should be able to load data and by writing our own functions calculate the probabilities of Algorithm is correct, predict defect given module has defect, predict defect given modules has no defect, and module has defect given predict defect.

1.2 Summary Table

Create the summary table (TABLE SIA3.2) found on page 125. Using \(\LaTeX\) construct the formulae for

1. Accuracy
2. Detection rate
3. False alarm rate
4. Precision

\(1. Accuracy: P(Algorithm is correct) = \frac{(a+d)}{(a+b+c+d)}\)

\(2. Detection Rate: P(predict defect|module has defect)=\frac{d}{(b+d)}\)

\(3. Fals alarm Rate: P(predict defect|module has no defect)=\frac{c}{(a+c)}\)

\(4. Precision: P(module has defect|predict defect)=\frac{d}{(d+c)}\)

2 R functions

Using the above definitions make R functions that will create the required probabilities, please remove eval=FALSE when creating the functions:

1. I am going to do is first I am going to load the data file into an object name collected.data.

2. Definition of a,b,c, and d is as below:

which is showing which method is predicting if there is any defect or not and if there is actually a defect.

3. Continue with that I am going to count the situation a,b,c, and d for each method

#Loading data to an object under the name of collected.data
collected.data=read.csv("SWDEFECTS.csv", header = TRUE)

n=with(collected.data, collected.data[,"defect"]) #putting defect into an object
vg10=with(collected.data, collected.data[,"predict.vg.10"]) #creating a vector for vg.10 method
evg14.5=with(collected.data, collected.data[,"predict.evg.14.5"]) ##creating a vector for evg.14.5 method
ivg9.2=with(collected.data, collected.data[,"predict.ivg.9.2"]) #creating a vector for ivg.9.2 method
loc50=with(collected.data, collected.data[,"predict.loc.50"]) #creating a vector for loc.50 method
summary(n) #Summary of data file

##    Mode   FALSE    TRUE 
## logical     449      49

length(n)  #Length data file

## [1] 498

vg10.a=0   #vg10.a is the initial value of the method vg.10 that predicts no defect and there is no defect
for (i in 1:length(n)){
  
  if (vg10[i]=="no" & n[i]=="FALSE")
  {
    vg10.a=vg10.a+1
  }
}
vg10.a #It shows how many FALSE defects there is when the algorithm vg.10 says also there is no defect

## [1] 397

vg10.b=0 #vg10.b is the initial value of the method vg.10 that predicts no defect but there is defects
for (i in 1:length(n)){
  
  if (vg10[i]=="no" & n[i]=="TRUE")
  {
    vg10.b=vg10.b+1
  }
}
vg10.b #Number of no defect predictions but actually there is defect

## [1] 35

vg10.c=0 #vg10.c is the initial value of the method vg.10 that predicts there is defect but there is no defect
for (i in 1:length(n)){
  
  if (vg10[i]=="yes" & n[i]=="FALSE")
  {
    vg10.c=vg10.c+1
  }
}
vg10.c #By Defining counter, this is the total number of data that have been predicted to have problem but it did not have problem using vg.10 method

## [1] 52

vg10.d=0 #vg10.d is the initial value of the method vg.10 that predicts there is defect and there are defects
for (i in 1:length(n)){
  
  if (vg10[i]=="yes" & n[i]=="TRUE")
  {
    vg10.d=vg10.d+1
  }
}
vg10.d #By Defining counter, this is the total number of data that have been predicted to have problem and it did have problem using vg.10 method

## [1] 14

evg14.5a=0 #evg14.5a is the initial value of the method evg14.5 that predicts no defect and there is no defect
for (i in 1:length(n))
  {
  
  if (evg14.5[i]=="no" & n[i]=="FALSE")
  {
    evg14.5a=evg14.5a+1
  }
}
evg14.5a #By Defining counter, this is the total number of data that have been predicted not to have problem and it did not have problem using evg14.5 method

## [1] 441

evg14.5b=0 #evg14.5b is the initial value of the method evg14.5 that predicts no defect but there are defects
for (i in 1:length(n))
  {
  
  if (evg14.5[i]=="no" & n[i]=="TRUE")
  {
    evg14.5b=evg14.5b+1
  }
}
evg14.5b #By Defining counter, this is the total number of data that have been predicted not to have problem but it did have problem using evg14.5 method

## [1] 47

evg14.5c=0 #evg14.5c is the initial value of the method evg14.5 that predicts there is defect but there is no defect
for (i in 1:length(n))
  {
  
  if (evg14.5[i]=="yes" & n[i]=="FALSE")
  {
    evg14.5c=evg14.5c+1
  }
}
evg14.5c #By Defining counter, this is the total number of data that have been predicted to have problem but it did not have problem using evg14.5 method

## [1] 8

evg14.5d=0 #evg14.5d is the initial value of the method evg14.5 that predicts there is defect and there are defects
for (i in 1:length(n))
  {
  
  if (evg14.5[i]=="yes" & n[i]=="TRUE")
  {
    evg14.5d=evg14.5d+1
  }
}
evg14.5d #By Defining counter, this is the total number of data that have been predicted to have problem but and it did have problem using evg14.5 method

## [1] 2

ivg9.2a=0 #ivg9.2a is the initial value of the method ivg9.2 that predicts no defect and there is no defect
for (i in 1:length(n))
  {
  
  if (ivg9.2[i]=="no" & n[i]=="FALSE")
  {
    ivg9.2a=ivg9.2a+1
  }
}
ivg9.2a #By Defining counter, this is the total number of data that have been predicted not to have problem and it did not have problem using ivg9.2 method

## [1] 422

ivg9.2b=0 #ivg9.2b is the initial value of the method ivg9.2 that predicts no defect but there are defects
for (i in 1:length(n))
  {
  
  if (ivg9.2[i]=="no" & n[i]=="TRUE")
  {
    ivg9.2b=ivg9.2b+1
  }
}
ivg9.2b #By Defining counter, this is the total number of data that have been predicted not to have problem but it did have problem using ivg9.2 method

## [1] 38

ivg9.2c=0 #ivg9.2c is the initial value of the method ivg9.2 that predicts there is defect but there is no defect
for (i in 1:length(n))
  {
  
  if (ivg9.2[i]=="yes" & n[i]=="FALSE")
  {
    ivg9.2c=ivg9.2c+1
  }
}
ivg9.2c #By Defining counter, this is the total number of data that have been predicted to have problem but it did not have problem using ivg9.2 method

## [1] 27

ivg9.2d=0 #ivg9.2d is the initial value of the method ivg9.2 that predicts there is defect and there are defects
for (i in 1:length(n))
  {
  
  if (ivg9.2[i]=="yes" & n[i]=="TRUE")
  {
    ivg9.2d=ivg9.2d+1
  }
}
ivg9.2d #By Defining counter, this is the total number of data that have been predicted to have problem and it did have problem using ivg9.2 method

## [1] 11

loc50.a=0 #loc50.a is the initial value of the method loc50 that predicts no defect and there is no defect
for (i in 1:length(n))
  {
  
  if (loc50[i]=="no" & n[i]=="FALSE")
  {
    loc50.a=loc50.a+1
  }
}
loc50.a #By Defining counter, this is the total number of data that have been predicted not to have problem and it did not have problem using loc50 method

## [1] 400

loc50.b=0 #loc50.b is the initial value of the method loc50 that predicts no defect but there is defects
for (i in 1:length(n))
  {
  
  if (loc50[i]=="no" & n[i]=="TRUE")
  {
    loc50.b=loc50.b+1
  }
}
loc50.b #By Defining counter, this is the total number of data that have been predicted not to have problem but it did have problem using loc50 method

## [1] 29

loc50.c=0 #loc50.c is the initial value of the method loc50 that predicts there is defect but there is no defect
for (i in 1:length(n))
  {
  
  if (loc50[i]=="yes" & n[i]=="FALSE")
  {
    loc50.c=loc50.c+1
  }
}
loc50.c #By Defining counter, this is the total number of data that have been predicted to have problem but it did not have problem using loc50 method

## [1] 49

loc50.d=0 #loc50.d is the initial value of the method loc50 that predicts there is defect and there are defects
for (i in 1:length(n))
  {
  
  if (loc50[i]=="yes" & n[i]=="TRUE")
  {
    loc50.d=loc50.d+1
  }
}
loc50.d #By Defining counter, this is the total number of data that have been predicted to have problem and it did have problem using loc50 method

## [1] 20

2.1 Accuracy Function

acc=function(a,b,c,d)
{
(a+d)/(a+b+c+d)
}

2.2 Detection Function

detect=function(b,d)
{
  d/(b+d)
}

2.3 False Alarm Rate Function

falarm=function(a,c)
{
  c/(a+c)
}

2.4 Precision Function

prec=function(c,d)
{
  d/(c+d)
}

3 Create the tables in Figure SIA3.1

3.1 Prediction vg.10 vs defect

swd=collected.data
head(swd)

tab=with(swd, table(predict.vg.10,defect))
barplot(tab, beside=TRUE, leg=TRUE)

tab2=addmargins(tab)
tab2

##              defect
## predict.vg.10 FALSE TRUE Sum
##           no    397   35 432
##           yes    52   14  66
##           Sum   449   49 498

3.2 Prediction evg.14.5 vs defect

swd=collected.data
head(swd)

tab=with(swd, table(predict.evg.14.5,defect))
barplot(tab, beside=TRUE, leg=TRUE)

tab2=addmargins(tab)
tab2

##                 defect
## predict.evg.14.5 FALSE TRUE Sum
##              no    441   47 488
##              yes     8    2  10
##              Sum   449   49 498

3.3 Prediction ivg.9.2 vs defect

swd=collected.data
head(swd)

tab=with(swd, table(predict.ivg.9.2,defect))
barplot(tab, beside=TRUE, leg=TRUE)

tab2=addmargins(tab)
tab2

##                defect
## predict.ivg.9.2 FALSE TRUE Sum
##             no    422   38 460
##             yes    27   11  38
##             Sum   449   49 498

3.4 Prediction loc.50 vs defect

swd=collected.data
head(swd)

tab=with(swd, table(predict.loc.50,defect))
barplot(tab, beside=TRUE, leg=TRUE)

tab2=addmargins(tab)
tab2

##               defect
## predict.loc.50 FALSE TRUE Sum
##            no    400   29 429
##            yes    49   20  69
##            Sum   449   49 498

4 Create the table on page 127, TABLE SIA3.3

4.1 Table and Barplot with Values

If we consider the initial value that we calculated a,b,c, and d for each method then we would have a bar plot and the SIA3.3 table as below:

vg10.a

## [1] 397

vg10.b

## [1] 35

vg10.c

## [1] 52

vg10.d

## [1] 14

evg14.5a

## [1] 441

evg14.5b

## [1] 47

evg14.5c

## [1] 8

evg14.5d

## [1] 2

ivg9.2a

## [1] 422

ivg9.2b

## [1] 38

ivg9.2c

## [1] 27

ivg9.2d

## [1] 11

loc50.a

## [1] 400

loc50.b

## [1] 29

loc50.c

## [1] 49

loc50.d

## [1] 20

a2=acc(vg10.a,vg10.b,vg10.c,vg10.d)
a3=acc(evg14.5a,evg14.5b, evg14.5c, evg14.5d)
a4=acc(ivg9.2a,ivg9.2b,ivg9.2c,ivg9.2d)
a1=acc(loc50.a,loc50.b,loc50.c,loc50.d)

b2=detect(vg10.b,vg10.d)
b3=detect(evg14.5b,evg14.5d)
b4=detect(ivg9.2b,ivg9.2d)
b1=detect(loc50.b,loc50.d)

c2=falarm(vg10.a,vg10.c)
c3=falarm(evg14.5a,evg14.5c)
c4=falarm(ivg9.2a,ivg9.2c)
c1=falarm(loc50.a,loc50.c)

d2=prec(vg10.c,vg10.d)
d3=prec(evg14.5c,evg14.5d)
d4=prec(ivg9.2c,ivg9.2d)
d1=prec(loc50.c,loc50.d)

probs=c("Accuracy","Detection Rate","False Alarm Rate", "Precision")
  mths = c("Lines of Code", "Cyclomatic complexity", "Essential complexity", "Design complexity")
  
  alltab = matrix(c(a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4,d1,d2,d3,d4),nr=4,nc=4,dimnames=list(mths,probs))
  
  alltab

##                        Accuracy Detection Rate False Alarm Rate Precision
## Lines of Code         0.8433735     0.40816327       0.10913140 0.2898551
## Cyclomatic complexity 0.8253012     0.28571429       0.11581292 0.2121212
## Essential complexity  0.8895582     0.04081633       0.01781737 0.2000000
## Design complexity     0.8694779     0.22448980       0.06013363 0.2894737

barplot(alltab, ylab="Probabilities", beside=TRUE, col=rainbow(20))

4.2 Defining the function

Defining the function that gives the table as SIA3.3 needs 16 input; the reason for that is we have 4 methods which for each method we should consider 4 output that two of them the method predicts defect which for one of them it is correct and for two of them predicts no defect that also in this case only of them is correct. so \(4\times4=16\) input is needed to form the table. The function is as below:

mytable=function(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p)
  {
vg10.a=a
vg10.b=b
vg10.c=c
vg10.d=d
evg14.5a=e
evg14.5b=f
evg14.5c=g
evg14.5d=h
ivg9.2a=i
ivg9.2b=j
ivg9.2c=k
ivg9.2d=l
loc50.a=m
loc50.b=n
loc50.c=o
loc50.d=p
  
a2=acc(vg10.a,vg10.b,vg10.c,vg10.d)
a3=acc(evg1.5a,evg1.5b, evg1.5c, evg1.5d)
a4=acc(ivg9.2a,ivg9.2b,ivg9.2c,ivg9.2d)
a1=acc(loc50.a,loc50.b,loc50.c,loc50.d)

b1=detect(vg10.b,vg10.d)
b2=detect(evg1.5b,evg1.5d)
b3=detect(ivg9.2b,ivg9.2d)
b4=detect(loc50.b,loc50.d)

c1=falarm(vg10.a,vg10.c)
c2=falarm(evg1.5a,evg1.5c)
c3=falarm(ivg9.2a,ivg9.2c)
c4=falarm(loc50.a,loc50.c)

d1=prec(vg10.c,vg10.d)
d2=prec(evg1.5c,evg1.5d)
d3=prec(ivg9.2c,ivg9.2d)
d4=prec(loc50.c,loc50.d)

probs=c("Accuracy","Detection Rate","False Alarm Rate", "Precision")
  mths = c("Lines of Code", "Cyclomatic complexity", "Essential complexity", "Design complexity")
  alltab = matrix(c(a1,b1,c1,d1,a2,b2,c2,d2,a3,b3,c3,d3,a4,b4,c4,d4),nr=4,nc=4,dimnames=list(mths,probs) )
  
barplot(alltab, ylab="probs", beside=TRUE, col=rainbow(20))
}